Jack's hat collection

Question

Jack's hat collection contains striped hats and spotted hats. The ratio of spotted hats to the total number of hats is 2:7. 

A) Jack picks a hat to wear at random. What is the probability it will be a str hat? 

B) What is the ratio of spotted hats to striped hats?

C) Jack throws away 5 spotted hats. The ratio of spotted to striped hats is now 1:2. How many spotted hats does Jack have?

 

Answer 1

A: Proportions are spotted 2, striped 5, so probability (striped hat) is 5/7

 

B: spotted hats:striped hats = 2/5

 

C: assume counts are spotted 2x, striped 5x; after discarding 5 spotted hats, there are 2x-5 remaining(spotted).

Then spotted hats:striped hats = (2x-5)/5x = ½.

 

Just solve the above equation for x and then the #of spotted hats (2x-5) can be stated.  NB: it must be an integer > 0.